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Class of operator mapping
In mathematics, a nonlocal operator is a mapping that maps a space of functions on a topological space to another space of functions on some domain in
Nonlocal_operator
Topics referred to by the same term
Non-local means, an algorithm in image processing for image denoising Nonlocal operator, which maps functions on a topological space to functions, in such
Nonlocal
Differential operator in mathematics
these eigenfunctions are the spherical harmonics. A nonlocal generalization of the Laplace operator is given by the fractional Laplacian ( − Δ ) α / 2
Laplace_operator
Mapping involving integration between function spaces
method List of transforms List of operators List of Fourier-related transforms Nachbin's theorem Nonlocal operator Reproducing kernel Symbolic integration
Integral_transform
Integral transform useful in probability theory, physics, and engineering
Tauberian theorem Laplace–Carson transform Moment-generating function Nonlocal operator Partial fraction decomposition Post's inversion formula Signal-flow
Laplace_transform
Mathematical transform that expresses a function of time as a function of frequency
Especially the image NGC 4622 Fourier transform m = 2. Nonlocal operator – Class of operator mapping Quadratic Fourier transform Quantum Fourier transform –
Fourier_transform
Deviations from local realism
In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not allow
Quantum_nonlocality
Nonlocal mathematical operator
powers of spatial derivatives. It is frequently used in the analysis of nonlocal partial differential equations, especially in geometry and diffusion theory
Fractional_Laplacian
Theoretical subdimensional particle
isolated fracton particles in type II models are associated with nonlocal operators with intricate fractal structure. The paradigmatic example of a type
Fracton (subdimensional particle)
Fracton_(subdimensional_particle)
Type of discrete calculus
then it can be interpreted as a discrete approximation of a related nonlocal operator in the continuum setting. A finite weighted graph G {\displaystyle
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
Branch of mathematical analysis
introduce fractional differential operators with non-singular nonlocal kernel. Their fractional differential operators are given below in Riemann–Liouville
Fractional_calculus
Gauge symmetry cannot be spontaneously broken
local operator can act as an order operator for confinement. Instead, to get around the theorem requires constructing nonlocal gauge invariant operators, whose
Elitzur's_theorem
Image denoising algorithm
result. Anisotropic diffusion Digital image processing Noise reduction Nonlocal operator Signal processing Total variation denoising Bounded variation Total
Non-local_means
Italian mathematician
equations, the regularity of their solution, their phase transitions, nonlocal operators, and free boundary problems, with applications including population
Serena_Dipierro
Physics phenomenon
true nonlocality in quantum mechanics itself. Despite these reservations, the term nonlocality has become a widespread convention. The term nonlocality is
Quantum_entanglement
Field theory involving topological effects in physics
Sergei; Kapustin, Anton (2013). "Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories". arXiv:1307.4793 [hep-th]. Linker
Topological quantum field theory
Topological_quantum_field_theory
Quantum mechanical operator related to rotational symmetry
angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role
Angular_momentum_operator
Researcher in computational mechanics
Academic Press, 2020) Computational Methods Based on Peridynamics and Nonlocal Operators: Theory and Applications (with Timon Rabczuk and Huilong Ren, Springer
Xiaoying_Zhuang
Of a function, an additional effect besides returning a value
CiteSeerX 10.1.1.70.2096. The term Side effect refers to the modification of the nonlocal environment. Generally this happens when a function (or a procedure) modifies
Side effect (computer science)
Side_effect_(computer_science)
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
been argued to be a different kind of geometric phase as it is "neither nonlocal nor topological", depending only on local quantities along the nuclear
Aharonov–Bohm_effect
Quantum operator
operator, as it appears in quantum mechanics. With every physical rotation R {\displaystyle R} , we postulate a quantum mechanical rotation operator D
Rotation operator (quantum mechanics)
Rotation_operator_(quantum_mechanics)
Set of rules defining correctly structured programs
else except False finally for from global if import in is lambda None nonlocal not or pass raise return True try while with yield In addition, Python
Python_syntax_and_semantics
Interpretation of quantum mechanics
Broglie and David Bohm. The interpretation is deterministic and explicitly nonlocal: the velocity of any one particle depends on the value of the guiding equation
De_Broglie–Bohm_theory
Theorem in physics
"Bell on Bell's Theorem: The Changing Face of Nonlocality". In Bell, Mary; Gao, Shan (eds.). Quantum Nonlocality and Reality: 50 years of Bell's theorem. Cambridge
Bell's_theorem
Non-local formulation of continuum mechanics
Xiaoying (2023-02-15). Computational Methods Based on Peridynamics and Nonlocal Operators: Theory and Applications. Springer Nature. ISBN 978-3-031-20906-2
Peridynamics
Mathematical model of magnetism
fermionic variables, using a highly nonlocal transformation known as the Jordan-Wigner Transformation. A fermion creation operator on site j {\displaystyle j}
Transverse-field_Ising_model
Mathematical tool in quantum physics
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed
Density_matrix
French mathematician (born 1951)
definition and the properties of the principal eigenvalue of some nonlocal operators. J. Funct. Anal. 271 (2016), no. 10, 2701–2751. Berestycki, Henri;
Henri_Berestycki
Description of physical properties at the atomic and subatomic scale
explicitly nonlocal. It attributes not only a wave function to a physical system but also a real position, which evolves deterministically under a nonlocal guiding
Quantum_mechanics
); (Zanardi, P. (16 January 2026). "Exact link between nonlocal nonstabilizerness and operator entanglement". Physical Review A. 113 (1). American Physical
Paolo_Zanardi
Physical principle that only immediate surroundings can influence an object
these terms, quantum mechanics would allow weakly nonlocal correlations but not strong nonlocality. One of the main principles of quantum field theory
Principle_of_locality
quantum action principle Propagator Annihilation operator S-matrix Standard Model Local quantum physics Nonlocal Effective field theory Correlation function
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Method for solving certain nonlinear partial differential equations
differential operators of order greater than two and also to periodic problems. In higher space dimensions one has instead a "nonlocal" Riemann–Hilbert
Inverse_scattering_transform
Quantum mechanical operator interchanging particle states as arguments to a function
mechanics, the exchange operator P ^ {\displaystyle {\hat {P}}} , also known as permutation operator, is a quantum mechanical operator that acts on states
Exchange_operator
Representation of the control state of a computer program
programming; and threads. The Scheme programming language includes the control operator call-with-current-continuation (abbreviated as: call/cc) with which a Scheme
Continuation
Description of a quantum-mechanical system
but in addition a real position that evolves deterministically under a nonlocal guiding equation. The evolution of a physical system is given at all times
Schrödinger_equation
Class of partial differential equations
equation. In 2008, Walter Craig and Steven Weinstein proved that under a nonlocal constraint, the initial value problem is well-posed for initial data given
Ultrahyperbolic_equation
Constraints on possible particle properties
isn't a one particle state. Obviously, a nonlocal charge does not have a local 4-current and a theory with a nonlocal 4-momentum does not have a local stress–energy
Weinberg–Witten_theorem
Notation for quantum states
Dirac notation is a mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual spaces both in the finite-
Bra–ket_notation
Mathematical mapping in quantum mechanics
of the fermionic operators is nonlocal with respect to the bosonic operators because we have to deal with an entire chain of operators to the left of the
Jordan–Wigner_transformation
Formulation of quantum mechanics
quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are mostly constant with respect to time (an
Schrödinger_picture
S2CID 14123321. Collins, Daniel; Linden, Noah; Popescu, Sandu (2001-08-07). "Nonlocal content of quantum operations". Physical Review A. 64 (3) 032302. arXiv:quant-ph/0005102
List_of_quantum_logic_gates
Theorem constraining types of hidden-variable theories
is a complement to Bell's theorem. While Bell's theorem established nonlocality to be a feature of any hidden-variable theory that recovers the predictions
Kochen–Specker_theorem
Equation in physics
example) the Klein–Gordon equation, electric field screening in plasmas, and nonlocal granular fluidity in granular flow. The equation is [ Δ − λ 2 ] u ( r )
Screened_Poisson_equation
Branch of knowledge concerned with building intuition for quantum theory
physical world itself is "nonlocal" is a topic of debate, but the terminology of "quantum nonlocality" is commonplace. Nonlocality research efforts in quantum
Quantum_foundations
Quantum mechanical model
{x}}} is the position operator (given by x in the coordinate basis), and p ^ {\displaystyle {\hat {p}}} is the momentum operator (given by p ^ = − i ℏ
Quantum_harmonic_oscillator
View of quantum mechanics
picture. Whereas in the other two pictures either the state vector or the operators carry time dependence, in the interaction picture both carry part of the
Interaction_picture
restrictions on strategies Alice and Bob can choose from. For example, in nonlocal games and pseudo-telepathy games, Alice and Bob are allowed to share entanglement
Quantum_refereed_game
Interpretation of quantum mechanics
(2002-11-12). "No time loophole in Bell's theorem: The Hess-Philipp model is nonlocal". Proceedings of the National Academy of Sciences. 99 (23): 14632–14635
Local_hidden-variable_theory
Concept in quantum mechanics
that measurement on one of two entangled particles can appear to have a nonlocal effect on the other particle. Additional problems related to decoherence
Observer_(quantum_physics)
Quantum mechanics taking into account particles near or at the speed of light
Another problem, less obvious and more severe, is that it can be shown to be nonlocal and can even violate causality: if the particle is initially localized
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Angular momentum deriving from photon spin
Newton–Wigner position operator and related constructions, analogous definitions for massless particles have led to ambiguities, nonlocal expressions, or violations
Spin angular momentum of light
Spin_angular_momentum_of_light
Theorem in functional analysis
Harry; Toner, Ben (2011), "A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement", Communications in Mathematical
Grothendieck_inequality
Converting classical mechanics to quantum mechanics
interpreting the interacting fields and their associated potentials as operators of multiplication, provided the potential is written in the canonical
First_quantization
Concept in statistics
Cambridge University Press, ISBN 0-521-41711-2 Cohen, O. (1997-11-01). "Nonlocality of the original Einstein-Podolsky-Rosen state". Physical Review A. 56
Quasiprobability_distribution
Model of concurrent computation
scaling up concurrency both locally and nonlocally. Transparency: bridging the chasm between local and nonlocal concurrency. Transparency is currently
Actor_model
Mathematical structures that allow quantum mechanics to be explained
structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces. In brief, values of physical observables such as energy
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Wigner distribution function in physics as opposed to in signal processing
Since ⋆ {\displaystyle \star } -composition of functions is thoroughly nonlocal (the "quantum probability fluid" diffuses, as observed by Moyal), vestiges
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Historical critique of quantum mechanics
showed that quantum mechanics was nonlocal, and suggested that a hidden-variable theory could heal this nonlocality. On the other hand, David Bohm had
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Second-order partial differential equation
119-121. ISBN 978-1-108-42041-9. Chicone, C.; Mashhoon, B. (2011-11-20). "Nonlocal Gravity: Modified Poisson's Equation". Journal of Mathematical Physics
Laplace's_equation
Theorem in quantum mechanics
time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force F = − V ′ ( x ) {\displaystyle
Ehrenfest_theorem
Area of physical and philosophical debate
as whether quantum mechanics is deterministic or stochastic, local or nonlocal, which elements of quantum mechanics can be considered real, and what the
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
Principle of quantum mechanics
system. An eigenvector ψ i {\displaystyle \psi _{i}} for a mathematical operator, A ^ {\displaystyle {\hat {A}}} , has the equation A ^ ψ i = λ i ψ i {\displaystyle
Quantum_superposition
Type of differential equation
functions of a single variable. Stochastic partial differential equations and nonlocal equations are widely studied extensions of the "PDE" notion. More classical
Partial_differential_equation
Concept in quantum entanglement
quantum entanglement to eliminate the need for classical communications. A nonlocal game is said to display quantum pseudo-telepathy if players who can use
Quantum_pseudo-telepathy
Formulation of quantum mechanics
formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived
Matrix_mechanics
1405105 E. C. Aifantis, "On the gradient approach – Relation to Eringen’s nonlocal theory" International Journal of Engineering Science Volume 49, Issue 12
GRADELA
Fact that observing a situation changes it
term "observable" has gained a technical meaning, denoting a self-adjoint operator that represents the possible results of a random variable. Observer (special
Observer_effect_(physics)
Device to store or transfer information in quantum computing
Brennen; D. Song; C.J. Williams (2003). "Quantum-computer architecture using nonlocal interactions". Physical Review A. 67 (5) 050302. arXiv:quant-ph/0301012
Quantum_bus
Quantum mechanics mathematical equation
quantity at equilibrium temperature T {\displaystyle T} , described by the operator A ^ {\displaystyle {\hat {A}}} , can be evaluated as: ⟨ A ^ ⟩ = 1 Z 0 Tr
Kubo_formula
Interpretation of quantum mechanics
"Bell on Bell's Theorem: The Changing Face of Nonlocality". In Mary Bell; Shan Gao (eds.). Quantum Nonlocality and Reality: 50 years of Bell's theorem. Cambridge
Many-worlds_interpretation
Specific quantum state of a quantum harmonic oscillator
displacement. These states, expressed as eigenvectors of the lowering operator and forming an overcomplete family, were introduced in the early papers
Coherent_state
Mathematical description of quantum state
In this case, the operator corresponding to position (a multiplication operator in the position representation) and the operator corresponding to momentum
Wave_function
Part of a computer program where a given name binding is valid
a global or nonlocal (in Python 3) declaration prior to use, which allows accessing global variables even if there is a masking nonlocal variable, and
Scope_(computer_programming)
Property of certain dynamical systems
to nonlocal linearization, through the solution of associated integral equations. The basic idea of this method is to introduce a linear operator that
Integrable_system
American mathematical physicist
particularly the development of axiomatic S-matrix theory, the proofs of strong nonlocality properties,[citation needed] and the place of free will in the orthodox
Henry_Stapp
Hamiltonian operator for molecules
Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger
Molecular_Hamiltonian
Calculation rule in quantum mechanics
|\psi \rangle } (see Bra–ket notation), corresponds to a self-adjoint operator A {\displaystyle A} whose spectrum is discrete if: the measured result
Born_rule
Term in quantum field theory
fermions, (−1)F is a unitary, Hermitian, involutive operator where F is the fermion number operator. For the example of particles in the Standard Model
(−1)F
"Highly entangled" quantum state of 3 or more qubits
^{\otimes M}}{\sqrt {2}}}.} The GHZ experiment demonstrates quantum nonlocality with the GHZ state. In a GHZ experiment, first a GHZ state is prepared
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
Hungarian and American mathematician and physicist (1903–1957)
substantially different from that of classical physics, or must include nonlocality in apparent violation of special relativity. In a chapter of The Mathematical
John_von_Neumann
Physical fields obeying the Schrödinger equation
V ( x 1 , x 2 ) {\displaystyle V(x_{1},x_{2})} , the interaction is a nonlocal contribution to the action: S = ∫ x t ψ † ( i ∂ ∂ t + ∇ 2 2 m ) ψ − ∫ x
Schrödinger_field
Force resulting from the quantisation of a field
for fermions can be understood as the spectral asymmetry of the fermion operator (−1)F, where it is known as the Witten index. Alternatively, a 2005 paper
Casimir_effect
Quantum error correcting code
the quantum harmonic oscillator with conjugate position and momentum operators. By encoding logical qubits into a single optical mode, the GKP code demonstrates
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
Quantum mechanical statistic
proposing that the fundamental new quality introduced by quantum physics is nonlocality. The Schrödinger equation i ℏ ∂ ψ ∂ t = ( − ℏ 2 2 m ∇ 2 + V ) ψ {\displaystyle
Quantum_potential
Formulations of quantum mechanics
relate operators in one picture to the analogous operators in the others. Not all textbooks and articles make explicit which picture each operator comes
Dynamical_pictures
Foundational principle in quantum physics
formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits. An
Uncertainty_principle
Bra–ket notation The bra–ket notation is a way to represent the states and operators of a system by angle brackets and vertical bars, for example, | α ⟩ {\displaystyle
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Mathematical operators
Katugampola fractional operators are integral operators that generalize the Riemann–Liouville and the Hadamard fractional operators into a unique form. The
Katugampola fractional operators
Katugampola_fractional_operators
Connection between correlation functions and the S-matrix
generalized to cover bound states, by use of composite fields which are often nonlocal. Furthermore, the method, or variants thereof, have turned out to be also
LSZ_reduction_formula
Truths and principles of the study of matter, space, time and energy
measurement problem, and the role of observers. Implications of entanglement, nonlocality, and the quantum-classical relationship are also explored. Relativity:
Philosophy_of_physics
Interaction of a quantum system with a classical observer
to one of the vectors comprising the basis. A density operator is a positive-semidefinite operator on the Hilbert space whose trace is equal to 1. For each
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Reconstruction of quantum states based on measurements
important to realize that the optical mode of the signal state is created nonlocal only when the trigger photon impinges the photodetector (of the trigger
Quantum_tomography
Sensor implementation technique
Howard M. Wiseman; Akira Furusawa (24 March 2015). "Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements"
Homodyne_detection
Formulation of quantum mechanics
interpretation explains the Einstein–Podolsky–Rosen paradox without resorting to nonlocality. Some[who?] advocates of interpretations of quantum mechanics emphasizing
Path_integral_formulation
Theorem in quantum mechanics
1086/289140. S2CID 122885859. Heywood, Peter; Redhead, Michael L. G. (1983). "Nonlocality and the Kochen–Specker paradox". Foundations of Physics. 13 (5): 481–499
Gleason's_theorem
Lowest possible energy of a quantum system or field
equation for a field operator, we must include the vacuum field, which is the homogeneous part of the solution for the field operator. In fact we can show
Zero-point_energy
Relativistic quantum mechanical wave equation
The Dirac equation then becomes an operator equation describing the state-independent evolution of the operator-valued spinor field ( i ∂ / − m ) ψ ^
Dirac_equation
Theoretical upper limit to non-local correlations in quantum mechanics
Anthony J.; Winter, Andreas (2007-10-30). "Quantum Nonlocality and Beyond: Limits from Nonlocal Computation". Physical Review Letters. 99 (18) 180502
Tsirelson's_bound
Programming construct
def Accumulator(n: int) -> Callable[[int], int]: def inc(x: int) -> int: nonlocal n: int n += x return n return inc In Ruby, several objects can be considered
Function_object
NONLOCAL OPERATOR
NONLOCAL OPERATOR
Girl/Female
Indian, Sanskrit
Name of Lord Shiva; The Operator; One who Maintains Balance Between Life and Death
Surname or Lastname
English
English : from the Old Norse female personal name Gunvǫr, composed of the elements gunn ‘battle’ + vǫr, the feminine form of varr ‘defender’, or possibly from the Old Norse male personal name Gunnarr.English : occupational name for an operator of heavy artillery (see Gunn).Americanized spelling of German Gönner, a habitational name for someone from any of numerous places named Gönne.
NONLOCAL OPERATOR
NONLOCAL OPERATOR
Girl/Female
Arabic, Muslim
One of the Solar Planet
Girl/Female
Christian, Indian
Wonderful; Pretty; Wheat
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Light of the World
Girl/Female
Arabic, Muslim, Sindhi
Repentant
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Lord Vishnu; Lover of Wealth
Male
German
(Russian ИÑаак): German and Russian form of Greek Isaák, ISAAK means "he will laugh."Â
Boy/Male
Muslim/Islamic
The year consisting of twelve months
Girl/Female
Australian, Gujarati, Hindu, Indian
Jewellery
Boy/Male
Muslim
Iranian poet, Tent
Surname or Lastname
English
English : from a medieval vernacular short form of the personal name Pascal, Latin Paschalis (see Pascal).
NONLOCAL OPERATOR
NONLOCAL OPERATOR
NONLOCAL OPERATOR
NONLOCAL OPERATOR
NONLOCAL OPERATOR
v. t.
To utter in a low and nonvocal tone; to say under the breath; hence, to mention privately and confidentially, or in a whisper.
n.
Same as Wiver. X () X, the twenty-fourth letter of the English alphabet, has three sounds; a compound nonvocal sound (that of ks), as in wax; a compound vocal sound (that of gz), as in example; and, at the beginning of a word, a simple vocal sound (that of z), as in xanthic. See Guide to Pronunciation, // 217, 270, 271.
a.
Uttered, as an element of speech, without tone, or proper vocal sound; voiceless; unintonated; nonvocal; atonic; whispered; aspirated; sharp; hard, as f, p, s, etc.; -- opposed to sonant. See Guide to Pronunciation, //169, 179, 180.
a.
See Gimmal. K () the eleventh letter of the English alphabet, is nonvocal consonant. The form and sound of the letter K are from the Latin, which used the letter but little except in the early period of the language. It came into the Latin from the Greek, which received it from a Phoenician source, the ultimate origin probably being Egyptian. Etymologically K is most nearly related to c, g, h (which see).
n.
A quantity of explosives anchored in a channel, beneath the water, or set adrift in a current, and so arranged that they will be exploded when touched by a vessel, or when an electric circuit is closed by an operator on shore.
n.
A vocal sound; specifically, a purely vocal element of speech, unmodified except by resonance; a vowel or a diphthong; a tonic element; a tonic; -- distinguished from a subvocal, and a nonvocal.
n.
A nonvocal consonant.
n.
A nonsonant or nonvocal consonant.
a.
Without voice; voiceless; nonvocal.
superl.
Uttered in a whisper, or with the breath alone, without voice, as certain consonants, such as p, k, t, f; surd; nonvocal; aspirated.
n.
An element of speech entirely destitute of vocality, or produced by the breath alone; a nonvocal or surd consonant; a breathing.
a.
Pertaining to or containing, ozone. P () the sixteenth letter of the English alphabet, is a nonvocal consonant whose form and value come from the Latin, into which language the letter was brought, through the ancient Greek, from the Phoenician, its probable origin being Egyptian. Etymologically P is most closely related to b, f, and v; as hobble, hopple; father, paternal; recipient, receive. See B, F, and M.
n.
The immovable union of two joints of a crinoidal arm. T () the twentieth letter of the English alphabet, is a nonvocal consonant. With the letter h it forms the digraph th, which has two distinct sounds, as in thin, then. See Guide to Pronunciation, //262-264, and also //153, 156, 169, 172, 176, 178-180.
a.
Uttered, as an element of speech, with tone or proper vocal sound, as distinguished from mere breath sound; intonated; voiced; tonic; the opposite of nonvocal, or surd; -- sid of the vowels, semivowels, liquids, and nasals, and particularly of the consonants b, d, g hard, v, etc., as compared with their cognates p, t, k, f, etc., which are called nonvocal, surd, or aspirate.
n.
Same as Eisel. F () F is the sixth letter of the English alphabet, and a nonvocal consonant. Its form and sound are from the Latin. The Latin borrowed the form from the Greek digamma /, which probably had the value of English w consonant. The form and value of Greek letter came from the Phoenician, the ultimate source being probably Egyptian. Etymologically f is most closely related to p, k, v, and b; as in E. five, Gr. pe`nte; E. wolf, L. lupus, Gr. ly`kos; E. fox, vixen ; fragile, break; fruit, brook, v. t.; E. bear, L. ferre. See Guide to Pronunciation, // 178, 179, 188, 198, 230.
n.
An instrument for writing by means of type, a typewheel, or the like, in which the operator makes use of a sort of keyboard, in order to obtain printed impressions of the characters upon paper.
n.
An elementary sound produced by the breath alone; a surd, or nonvocal consonant; as, f, th in thin, etc.
v. t.
To utter without vocality, as the nonvocal consonants.
a.
Not vocal; destitute of tone.
a.
Having the same foci; as, confocal quadrics.